Three-dimensional fracture abundance evaluation of subsurface formations

ABSTRACT

A method, apparatus, and program product evaluate fracture abundance in a subsurface formation by modeling a fracture network in a three-dimensional volume using geometric primitives. A fracture abundance parameter, e.g., a P 32  fracture density, may be determined in part based upon the combined areas of the primitives with cells of a three-dimensional grid.

BACKGROUND

Reservoir modeling and simulation are commonly used in the oil & gasindustry to model the structure and/or properties of a subsurfaceformation, e.g., of the type containing recoverable hydrocarbons, aswell as to model the flow of fluids such as recoverable hydrocarbonsthroughout such a formation. Reservoir modeling and simulation may beused during various phases of exploration and production, including, forexample, to attempt to predict the location, quantity and/or value ofrecoverable hydrocarbons, to plan the development of wells forcost-effectively extracting hydrocarbons from the subsurface formation,and to guide future and/or ongoing production and development decisions.

Many subsurface formations include some degree of fracturing, i.e., thepresence of faults, joints, cracks and other discontinuities thatseparate rock within the subsurface formation. Fractures generally havegreater permeability and porosity than solid rock, so accounting for theeffects of fractures is generally desirable for accurate fluid flowsimulation. In this regard, a number of different fracture abundancemeasures have been proposed to represent the relative amount offracturing within a subsurface formation, including, for example,fracture density, fracture intensity, fracture porosity, etc. Someconventional approaches, for example, calculate a fracture density as aP₁₀ value (number of fractures per unit length along a scanline) fromwells. In addition, in some approaches a P₃₂ value (sum of fracture areaper unit volume) is inferred from the P₁₀ value by making an assumptionthat fractures entirely intersect a borehole as well as corrected fromborehole deviation and then using a statistical method to interpolateP₃₂ in a three-dimensional (3D) grid as an input for Discrete FractureNetwork (DFN) generation.

The P₃₂ value is desirable in many applications because fracture size isaccounted for in the value and does not depend on borehole trajectory.However, accurate fracture sizes within a borehole are generallydifficult to obtain from borehole images and core logging, and generallyresult in the calculation of only a “relative” P₃₂ measurement fromwells. Furthermore, interpolation of this measurement generally createslarge uncertainties within the 3D grid that generally cannot be easilyquantified.

Therefore, a need exists in the art for improved evaluation of P₃₂ andother fracture abundance parameters, and in particular, an improvedevaluation having greater accuracy and/or greater computationalefficiency than convention approaches.

SUMMARY

The embodiments disclosed herein provide a method, apparatus, andprogram product that evaluate fracture abundance in a subsurfaceformation by defining a fracture network within multiple cells of athree-dimensional model of the subsurface formation using multiplegeometric primitives, determining an area of the geometric primitiveswithin at least a subset of the cells by summing areas of individualgeometric primitives within each of the subset of cells, and determininga fracture abundance parameter for the fracture network from thedetermined area of the geometric primitives.

In some embodiments, defining the fracture network includes expandingeach of multiple two-dimensional polylines representing fractures in thesubsurface formation within a respective containing plane. In addition,in some embodiments, defining the fracture network further includesrepresenting each two-dimensional polyline by multiple geometricprimitives disposed in the respective containing plane. In someembodiments, the two-dimensional polylines are disposed in a commonplane, and the respective containing planes extend in a same directionrelative to the common plane, and in some embodiments, the respectivecontaining planes are substantially orthogonal to the common plane.Further, in some embodiments, the respective containing planes aresubstantially vertical and the common plane is substantially horizontal,while in some embodiments, the respective containing planes extend indifferent directions relative to the common plane.

In some embodiments, expanding each of the two-dimensional polylinesincludes using an aspect ratio to constrain expansion of each of thetwo-dimensional polylines within the respective containing planesrelative to fracture length, and in some embodiments, each of thegeometric primitives is a triangular element. Further, in someembodiments, expanding each of the two-dimensional polylines includesexpanding a first two-dimensional polyline among the two-dimensionalpolylines into a substantially rectangular shape represented by firstand second triangular elements defined by four nodes, while in someembodiments, expanding each of the two-dimensional polylines includesexpanding a first two-dimensional polyline among the two-dimensionalpolylines into a substantially elliptical shape represented by twelvetriangular elements defined by thirteen nodes. In some embodiments, thesubstantially elliptical shape is a substantially circular shape.

In addition, in some embodiments, determining the area of the geometricprimitives within the subset of the cells includes clipping individualgeometric primitives that are partially within each of the subset ofcells. In addition, in some embodiments, determining the area of thegeometric primitives within the subset of the cells further includesorganizing the geometric primitives within a spatially-organized datastructure and accessing the spatially-organized data structure whensumming areas of individual geometric primitives within each of thesubset of cells to determine which of the geometric primitives are atleast partially within each of the subset of cells.

In some embodiments, determining the fracture abundance parameterincludes determining a fracture density within each of the subset ofcells by dividing the summed areas of individual geometric primitivestherein by a volume thereof, and in some embodiments, determining thefracture abundance parameter includes determining a directly-calculatedP₃₂ fracture density within each of the subset of cells by dividing thesummed areas of individual geometric primitives therein by a volumethereof.

Some embodiments also include running a fluid flow simulation using thedetermined fracture abundance parameter to estimate fluid flow throughthe fracture network. Further, some embodiments also include performingan oilfield operation based upon a result of the fluid flow simulation.

Some embodiments may also include an apparatus including at least oneprocessing unit and program code configured upon execution by the atleast one processing unit to evaluate fracture abundance in a subsurfaceformation in any of the manners discussed herein. Some embodiments mayalso include a program product including a computer readable medium andprogram code stored on the computer readable medium and configured uponexecution by at least one processing unit to evaluate fracture abundancein a subsurface formation in any of the manners discussed herein.

These and other advantages and features, which characterize theinvention, are set forth in the claims annexed hereto and forming afurther part hereof. However, for a better understanding of theinvention, and of the advantages and objectives attained through itsuse, reference should be made to the Drawings, and to the accompanyingdescriptive matter, in which there is described example embodiments ofthe invention. This summary is merely provided to introduce a selectionof concepts that are further described below in the detaileddescription, and is not intended to identify key or essential featuresof the claimed subject matter, nor is it intended to be used as an aidin limiting the scope of the claimed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example hardware and softwareenvironment for a data processing system in accordance withimplementation of various technologies and techniques described herein.

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield havingsubterranean formations containing reservoirs therein in accordance withimplementations of various technologies and techniques described herein.

FIG. 3 illustrates a schematic view, partially in cross section of anoilfield having a plurality of data acquisition tools positioned atvarious locations along the oilfield for collecting data from thesubterranean formations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 4 illustrates a production system for performing one or moreoilfield operations in accordance with implementations of varioustechnologies and techniques described herein.

FIG. 5 is a flowchart illustrating an example sequence of operations forperforming fracture abundance evaluation in the data processing systemof FIG. 1.

FIG. 6 is a flowchart illustrating an example sequence of operations fordefining a fracture network in the data processing system of FIG. 1.

FIG. 7A illustrates an example fracture map, and FIGS. 7B, 7C and 7Dillustrate growing the fractures in the example fracture map of FIG. 7Ainto rectangular, elliptical, and circular shapes, respectively.

FIG. 8 is a flowchart illustrating an example sequence of operations fordetermining a P₃₂ value a fracture network in the data processing systemof FIG. 1.

FIG. 9 illustrates three-dimensional views of a full grid and ahorizontal layer through a grid with a fracture abundance parameterdisplayed therein.

FIG. 10 illustrates calculating a length of a line in a two-dimensionalspace using projection.

FIG. 11 illustrates calculating an area of a primitive in a cell usingprojection.

FIG. 12 is a flowchart illustrating an example sequence of operationsfor determining a P₃₂ value using geometric primitive projection in thedata processing system of FIG. 1.

FIG. 13 is a flowchart illustrating an example sequence of operationsfor performing fracture abundance evaluation in the data processingsystem of FIG. 1, and based in part upon geomechanical simulation ofmechanical properties.

FIG. 14 illustrates three-dimensional views of a three-dimensionalfracture network grown from a balance energy operation, and a verticalsection including a directly-calculated P32.

FIG. 15 functionally illustrates an example vertical cross-sectionthrough a fractured subsurface formation with multiple wells extendingthrough the subsurface formation.

DETAILED DESCRIPTION

The herein-described embodiments utilize a number of techniques toevaluate fracture abundance in a subsurface formation, e.g., a region orvolume of the Earth such as a volume potentially incorporatingrecoverable hydrocarbons. Fracture abundance, in particular, may beevaluated using a three-dimensional fracture network defined using aplurality of geometric primitives such as triangular elements disposedwithin a three-dimensional volume, and the evaluation of fractureabundance may result in the generation of one or more fracture abundanceparameters for the subsurface formation. A fracture abundance parameter,within the context of the invention, may be any parameter that isindicative of the abundance or amount of fracturing in a subsurfacevolume, e.g., based on fracture intensity, fracture density, fractureporosity, etc. In some embodiments, a fracture abundance parameter maybe based, for example, on ratios between different dimensional values,e.g., various P_(XY) values, where x is the dimension of the measuredvalue or feature and y is the dimension of the sampling region. In theembodiments discussed below, for example, a fracture abundance parametermay be a P₃₂ value of fracture density, based on the sum of the areas offractures in a unit volume such as a grid cell. As other measurements orparameters may be used to represent relative amounts of fracturing in asubsurface volume, however, the invention is not limited to P₃₂ fracturedensity values.

Other variations and modifications will be apparent to one of ordinaryskill in the art.

Hardware and Software Environment

Turning now to the drawings, wherein like numbers denote like partsthroughout the several views, FIG. 1 illustrates an example dataprocessing system 10 in which the various technologies and techniquesdescribed herein may be implemented. System 10 is illustrated asincluding one or more computers 12, e.g., client computers, eachincluding a central processing unit (CPU) 14 including at least onehardware-based processor or processing core 16. CPU 14 is coupled to amemory 18, which may represent the random access memory (RAM) devicescomprising the main storage of a computer 12, as well as anysupplemental levels of memory, e.g., cache memories, non-volatile orbackup memories (e.g., programmable or flash memories), read-onlymemories, etc. In addition, memory 18 may be considered to includememory storage physically located elsewhere in a computer 12, e.g., anycache memory in a microprocessor or processing core, as well as anystorage capacity used as a virtual memory, e.g., as stored on a massstorage device 20 or on another computer coupled to a computer 12.

Each computer 12 also generally receives a number of inputs and outputsfor communicating information externally. For interface with a user oroperator, a computer 12 generally includes a user interface 22incorporating one or more user input/output devices, e.g., a keyboard, apointing device, a display, a printer, etc. Otherwise, user input may bereceived, e.g., over a network interface 24 coupled to a network 26,from one or more external computers, e.g., one or more servers 28 orother computers 12. A computer 12 also may be in communication with oneor more mass storage devices 20, which may be, for example, internalhard disk storage devices, external hard disk storage devices, storagearea network devices, etc.

A computer 12 generally operates under the control of an operatingsystem 30 and executes or otherwise relies upon various computersoftware applications, components, programs, objects, modules, datastructures, etc. For example, a petro-technical module or component 32executing within an exploration and production (E&P) platform 34 may beused to access, process, generate, modify or otherwise utilizepetro-technical data, e.g., as stored locally in a database 36 and/oraccessible remotely from a collaboration platform 38. Collaborationplatform 38 may be implemented using multiple servers 28 in someimplementations, and it will be appreciated that each server 28 mayincorporate a CPU, memory, and other hardware components similar to acomputer 12.

In one non-limiting embodiment, for example, E&P platform 34 mayimplemented as the PETREL Exploration & Production (E&P) softwareplatform, while collaboration platform 38 may be implemented as theSTUDIO E&P KNOWLEDGE ENVIRONMENT platform, both of which are availablefrom Schlumberger Ltd. and its affiliates. It will be appreciated,however, that the techniques discussed herein may be utilized inconnection with other platforms and environments, so the invention isnot limited to the particular software platforms and environmentsdiscussed herein.

In general, the routines executed to implement the embodiments disclosedherein, whether implemented as part of an operating system or a specificapplication, component, program, object, module or sequence ofinstructions, or even a subset thereof, will be referred to herein as“computer program code,” or simply “program code.” Program codegenerally comprises one or more instructions that are resident atvarious times in various memory and storage devices in a computer, andthat, when read and executed by one or more hardware-based processingunits in a computer (e.g., microprocessors, processing cores, or otherhardware-based circuit logic), cause that computer to perform the stepsembodying desired functionality. Moreover, while embodiments have andhereinafter will be described in the context of fully functioningcomputers and computer systems, those skilled in the art will appreciatethat the various embodiments are capable of being distributed as aprogram product in a variety of forms, and that the invention appliesequally regardless of the particular type of computer readable mediaused to actually carry out the distribution.

Such computer readable media may include computer readable storage mediaand communication media. Computer readable storage media isnon-transitory in nature, and may include volatile and non-volatile, andremovable and non-removable media implemented in any method ortechnology for storage of information, such as computer-readableinstructions, data structures, program modules or other data. Computerreadable storage media may further include RAM, ROM, erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), flash memory or other solidstate memory technology, CD-ROM, DVD, or other optical storage, magneticcassettes, magnetic tape, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to store thedesired information and which can be accessed by computer 10.Communication media may embody computer readable instructions, datastructures or other program modules. By way of example, and notlimitation, communication media may include wired media such as a wirednetwork or direct-wired connection, and wireless media such as acoustic,RF, infrared and other wireless media. Combinations of any of the abovemay also be included within the scope of computer readable media.

Various program code described hereinafter may be identified based uponthe application within which it is implemented in a specific embodimentof the invention. However, it should be appreciated that any particularprogram nomenclature that follows is used merely for convenience, andthus the invention should not be limited to use solely in any specificapplication identified and/or implied by such nomenclature. Furthermore,given the endless number of manners in which computer programs may beorganized into routines, procedures, methods, modules, objects, and thelike, as well as the various manners in which program functionality maybe allocated among various software layers that are resident within atypical computer (e.g., operating systems, libraries, API's,applications, applets, etc.), it should be appreciated that theinvention is not limited to the specific organization and allocation ofprogram functionality described herein.

Furthermore, it will be appreciated by those of ordinary skill in theart having the benefit of the instant disclosure that the variousoperations described herein that may be performed by any program code,or performed in any routines, workflows, or the like, may be combined,split, reordered, omitted, and/or supplemented with other techniquesknown in the art, and therefore, the invention is not limited to theparticular sequences of operations described herein.

Those skilled in the art will recognize that the example environmentillustrated in FIG. 1 is not intended to limit the invention. Indeed,those skilled in the art will recognize that other alternative hardwareand/or software environments may be used without departing from thescope of the invention.

Oilfield Operations

FIGS. 2A-2D illustrate simplified, schematic views of an oilfield 100having subterranean formation 102 containing reservoir 104 therein inaccordance with implementations of various technologies and techniquesdescribed herein. FIG. 2A illustrates a survey operation being performedby a survey tool, such as seismic truck 106.1, to measure properties ofthe subterranean formation. The survey operation is a seismic surveyoperation for producing sound vibrations. In FIG. 2A, one such soundvibration, sound vibration 112 generated by source 110, reflects offhorizons 114 in earth formation 116. A set of sound vibrations isreceived by sensors, such as geophone-receivers 118, situated on theearth's surface. The data received 120 is provided as input data to acomputer 122.1 of a seismic truck 106.1, and responsive to the inputdata, computer 122.1 generates seismic data output 124. This seismicdata output may be stored, transmitted or further processed as desired,for example, by data reduction.

FIG. 2B illustrates a drilling operation being performed by drillingtools 106.2 suspended by rig 128 and advanced into subterraneanformations 102 to form wellbore 136. Mud pit 130 is used to drawdrilling mud into the drilling tools via flow line 132 for circulatingdrilling mud down through the drilling tools, then up wellbore 136 andback to the surface. The drilling mud may be filtered and returned tothe mud pit. A circulating system may be used for storing, controlling,or filtering the flowing drilling muds. The drilling tools are advancedinto subterranean formations 102 to reach reservoir 104. Each well maytarget one or more reservoirs. The drilling tools are adapted formeasuring downhole properties using logging while drilling tools. Thelogging while drilling tools may also be adapted for taking core sample133 as shown.

Computer facilities may be positioned at various locations about theoilfield 100 (e.g., the surface unit 134) and/or at remote locations.Surface unit 134 may be used to communicate with the drilling toolsand/or offsite operations, as well as with other surface or downholesensors. Surface unit 134 is capable of communicating with the drillingtools to send commands to the drilling tools, and to receive datatherefrom. Surface unit 134 may also collect data generated during thedrilling operation and produces data output 135, which may then bestored or transmitted.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various oilfield operations as describedpreviously. As shown, sensor (S) is positioned in one or more locationsin the drilling tools and/or at rig 128 to measure drilling parameters,such as weight on bit, torque on bit, pressures, temperatures, flowrates, compositions, rotary speed, and/or other parameters of the fieldoperation. Sensors (S) may also be positioned in one or more locationsin the circulating system.

Drilling tools 106.2 may include a bottom hole assembly (BHA) (notshown), generally referenced, near the drill bit (e.g., within severaldrill collar lengths from the drill bit). The bottom hole assemblyincludes capabilities for measuring, processing, and storinginformation, as well as communicating with surface unit 134. The bottomhole assembly further includes drill collars for performing variousother measurement functions.

The bottom hole assembly may include a communication subassembly thatcommunicates with surface unit 134. The communication subassembly isadapted to send signals to and receive signals from the surface using acommunications channel such as mud pulse telemetry, electro-magnetictelemetry, or wired drill pipe communications. The communicationsubassembly may include, for example, a transmitter that generates asignal, such as an acoustic or electromagnetic signal, which isrepresentative of the measured drilling parameters. It will beappreciated by one of skill in the art that a variety of telemetrysystems may be employed, such as wired drill pipe, electromagnetic orother known telemetry systems.

Generally, the wellbore is drilled according to a drilling plan that isestablished prior to drilling. The drilling plan sets forth equipment,pressures, trajectories and/or other parameters that define the drillingprocess for the wellsite. The drilling operation may then be performedaccording to the drilling plan. However, as information is gathered, thedrilling operation may need to deviate from the drilling plan.Additionally, as drilling or other operations are performed, thesubsurface conditions may change. The earth model may also needadjustment as new information is collected

The data gathered by sensors (S) may be collected by surface unit 134and/or other data collection sources for analysis or other processing.The data collected by sensors (S) may be used alone or in combinationwith other data. The data may be collected in one or more databasesand/or transmitted on or offsite. The data may be historical data, realtime data, or combinations thereof. The real time data may be used inreal time, or stored for later use. The data may also be combined withhistorical data or other inputs for further analysis. The data may bestored in separate databases, or combined into a single database.

Surface unit 134 may include transceiver 137 to allow communicationsbetween surface unit 134 and various portions of the oilfield 100 orother locations. Surface unit 134 may also be provided with orfunctionally connected to one or more controllers (not shown) foractuating mechanisms at oilfield 100. Surface unit 134 may then sendcommand signals to oilfield 100 in response to data received. Surfaceunit 134 may receive commands via transceiver 137 or may itself executecommands to the controller. A processor may be provided to analyze thedata (locally or remotely), make the decisions and/or actuate thecontroller. In this manner, oilfield 100 may be selectively adjustedbased on the data collected. This technique may be used to optimizeportions of the field operation, such as controlling drilling, weight onbit, pump rates, or other parameters. These adjustments may be madeautomatically based on computer protocol, and/or manually by anoperator. In some cases, well plans may be adjusted to select optimumoperating conditions, or to avoid problems.

FIG. 2C illustrates a wireline operation being performed by wirelinetool 106.3 suspended by rig 128 and into wellbore 136 of FIG. 2B.Wireline tool 106.3 is adapted for deployment into wellbore 136 forgenerating well logs, performing downhole tests and/or collectingsamples. Wireline tool 106.3 may be used to provide another method andapparatus for performing a seismic survey operation. Wireline tool 106.3may, for example, have an explosive, radioactive, electrical, oracoustic energy source 144 that sends and/or receives electrical signalsto surrounding subterranean formations 102 and fluids therein.

Wireline tool 106.3 may be operatively connected to, for example,geophones 118 and a computer 122.1 of a seismic truck 106.1 of FIG. 2A.Wireline tool 106.3 may also provide data to surface unit 134. Surfaceunit 134 may collect data generated during the wireline operation andmay produce data output 135 that may be stored or transmitted. Wirelinetool 106.3 may be positioned at various depths in the wellbore 136 toprovide a survey or other information relating to the subterraneanformation 102.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, sensor S is positioned in wireline tool 106.3 tomeasure downhole parameters which relate to, for example porosity,permeability, fluid composition and/or other parameters of the fieldoperation.

FIG. 2D illustrates a production operation being performed by productiontool 106.4 deployed from a production unit or Christmas tree 129 andinto completed wellbore 136 for drawing fluid from the downholereservoirs into surface facilities 142. The fluid flows from reservoir104 through perforations in the casing (not shown) and into productiontool 106.4 in wellbore 136 and to surface facilities 142 via gatheringnetwork 146.

Sensors (S), such as gauges, may be positioned about oilfield 100 tocollect data relating to various field operations as describedpreviously. As shown, the sensor (S) may be positioned in productiontool 106.4 or associated equipment, such as christmas tree 129,gathering network 146, surface facility 142, and/or the productionfacility, to measure fluid parameters, such as fluid composition, flowrates, pressures, temperatures, and/or other parameters of theproduction operation.

Production may also include injection wells for added recovery. One ormore gathering facilities may be operatively connected to one or more ofthe wellsites for selectively collecting downhole fluids from thewellsite(s).

While FIGS. 2B-2D illustrate tools used to measure properties of anoilfield, it will be appreciated that the tools may be used inconnection with non-oilfield operations, such as gas fields, mines,aquifers, storage, or other subterranean facilities. Also, while certaindata acquisition tools are depicted, it will be appreciated that variousmeasurement tools capable of sensing parameters, such as seismic two-waytravel time, density, resistivity, production rate, etc., of thesubterranean formation and/or its geological formations may be used.Various sensors (S) may be located at various positions along thewellbore and/or the monitoring tools to collect and/or monitor thedesired data. Other sources of data may also be provided from offsitelocations.

The field configurations of FIGS. 2A-2D are intended to provide a briefdescription of an example of a field usable with oilfield applicationframeworks. Part, or all, of oilfield 100 may be on land, water, and/orsea. Also, while a single field measured at a single location isdepicted, oilfield applications may be utilized with any combination ofone or more oilfields, one or more processing facilities and one or morewellsites.

FIG. 3 illustrates a schematic view, partially in cross section ofoilfield 200 having data acquisition tools 202.1, 202.2, 202.3 and 202.4positioned at various locations along oilfield 200 for collecting dataof subterranean formation 204 in accordance with implementations ofvarious technologies and techniques described herein. Data acquisitiontools 202.1-202.4 may be the same as data acquisition tools 106.1-106.4of FIGS. 2A-2D, respectively, or others not depicted. As shown, dataacquisition tools 202.1-202.4 generate data plots or measurements208.1-208.4, respectively. These data plots are depicted along oilfield200 to demonstrate the data generated by the various operations.

Data plots 208.1-208.3 are examples of static data plots that may begenerated by data acquisition tools 202.1-202.3, respectively, however,it should be understood that data plots 208.1-208.3 may also be dataplots that are updated in real time. These measurements may be analyzedto better define the properties of the formation(s) and/or determine theaccuracy of the measurements and/or for checking for errors. The plotsof each of the respective measurements may be aligned and scaled forcomparison and verification of the properties.

Static data plot 208.1 is a seismic two-way response over a period oftime. Static plot 208.2 is core sample data measured from a core sampleof the formation 204. The core sample may be used to provide data, suchas a graph of the density, porosity, permeability, or some otherphysical property of the core sample over the length of the core. Testsfor density and viscosity may be performed on the fluids in the core atvarying pressures and temperatures. Static data plot 208.3 is a loggingtrace that generally provides a resistivity or other measurement of theformation at various depths.

A production decline curve or graph 208.4 is a dynamic data plot of thefluid flow rate over time. The production decline curve generallyprovides the production rate as a function of time. As the fluid flowsthrough the wellbore, measurements are taken of fluid properties, suchas flow rates, pressures, composition, etc.

Other data may also be collected, such as historical data, user inputs,economic information, and/or other measurement data and other parametersof interest. As described below, the static and dynamic measurements maybe analyzed and used to generate models of the subterranean formation todetermine characteristics thereof. Similar measurements may also be usedto measure changes in formation aspects over time.

The subterranean structure 204 has a plurality of geological formations206.1-206.4. As shown, this structure has several formations or layers,including a shale layer 206.1, a carbonate layer 206.2, a shale layer206.3 and a sand layer 206.4. A fault 207 extends through the shalelayer 206.1 and the carbonate layer 206.2. The static data acquisitiontools are adapted to take measurements and detect characteristics of theformations.

While a specific subterranean formation with specific geologicalstructures is depicted, it will be appreciated that oilfield 200 maycontain a variety of geological structures and/or formations, sometimeshaving extreme complexity. In some locations, generally below the waterline, fluid may occupy pore spaces of the formations. Each of themeasurement devices may be used to measure properties of the formationsand/or its geological features. While each acquisition tool is shown asbeing in specific locations in oilfield 200, it will be appreciated thatone or more types of measurement may be taken at one or more locationsacross one or more fields or other locations for comparison and/oranalysis.

The data collected from various sources, such as the data acquisitiontools of FIG. 3, may then be processed and/or evaluated. Generally,seismic data displayed in static data plot 208.1 from data acquisitiontool 202.1 is used by a geophysicist to determine characteristics of thesubterranean formations and features. The core data shown in static plot208.2 and/or log data from well log 208.3 are generally used by ageologist to determine various characteristics of the subterraneanformation. The production data from graph 208.4 is generally used by thereservoir engineer to determine fluid flow reservoir characteristics.The data analyzed by the geologist, geophysicist and the reservoirengineer may be analyzed using modeling techniques.

FIG. 4 illustrates an oilfield 300 for performing production operationsin accordance with implementations of various technologies andtechniques described herein. As shown, the oilfield has a plurality ofwellsites 302 operatively connected to central processing facility 354.The oilfield configuration of FIG. 4 is not intended to limit the scopeof the oilfield application system. Part or all of the oilfield may beon land and/or sea. Also, while a single oilfield with a singleprocessing facility and a plurality of wellsites is depicted, anycombination of one or more oilfields, one or more processing facilitiesand one or more wellsites may be present.

Each wellsite 302 has equipment that forms wellbore 336 into the earth.The wellbores extend through subterranean formations 306 includingreservoirs 304. These reservoirs 304 contain fluids, such ashydrocarbons. The wellsites draw fluid from the reservoirs and pass themto the processing facilities via surface networks 344. The surfacenetworks 344 have tubing and control mechanisms for controlling the flowof fluids from the wellsite to processing facility 354.

Three-Dimensional Fracture Abundance Evaluation

As noted above, evaluation of fracture abundance parameters such as P₃₂fracture density may be limited in conventional approaches due in partto difficulties associated with accurately accounting for fracture sizesfrom borehole or other formation data. Embodiments consistent with theinvention, on the other hand, may utilize a three-dimensional approachincorporating various features that facilitate evaluation of fractureabundance in a subsurface formation in a more computationally efficientand accurate manner than such approaches.

Embodiments consistent with the invention, in particular, may be basedin part upon a determination of the areas of geometric primitives thatare used to represent a fracture network within a three-dimensionalvolume, e.g., within a three-dimensional model of a subsurfaceformation. The geometric primitives may be implemented, for example, astwo-dimensional triangles defined by collections of three points in thethree-dimensional volume, although other two-dimensional shapes may beused as geometric primitives in other embodiments of the invention. Theareas furthermore may be determined on a subvolume-by-subvolume basis,e.g., with primitives that fall entirely within a subvolume having areascorresponding to the areas of the entire primitives, and with primitivesthat fall partially within a subvolume being clipped at the boundariesof the subvolume such that the areas are of the clipped portions of theprimitives. In some embodiments, for example, a fracture network may beoverlaid into a regular grid of cubic cells, and as such, areas ofprimitives representing a fracture network may be determined on acell-by-cell basis.

In the illustrated embodiments discussed hereinafter, the areas of eachof the primitives (or clipped portions thereof) within each cell may besummed, and then a ratio may be taken against the volume of each cell togenerate a “real” P₃₂ fracture density for each cell. In contrast withmany conventional approaches, the P₃₂ fracture density may be a moredirectly-calculated or “true” value rather than an inferred andinterpolated value, and may be used to better constrain and validate afracture network and/or to define correction factors to correct anyrelative P₃₂ values inferred from a borehole and/or interpolated in a 3Dgrid. As noted above, however, the techniques described herein may beused to calculate other fracture abundance parameters, so the inventionis not limited to the particular fracture density calculations discussedherein.

FIG. 5, for example, illustrates a sequence of operations 400 capable ofbeing implemented in data processing system 10 to evaluate fractureabundance within a subsurface formation. In block 402, a fracturenetwork may be defined within the cells of a three-dimensional modelusing a plurality of geometric primitives. As will become more apparentbelow, in some embodiments, a fracture network may be generated in partfrom outcrop and/or seismic data, which may be used to generatetwo-dimensional (2D) polylines. In addition, in some embodiments, thefracture network may be generated by growing or expanding the 2Dpolylines in one or more directions and representing the resultingshapes using geometric primitives, with all polylines grown in the samedirection (e.g., horizontally or vertically), or with differentpolylines grown in different directions. In other embodiments, afracture network may be generated manually (e.g., through a computerinterface) and/or based on collected data (e.g., from geomechanicalproperties).

A polyline, in this regard, may refer to a line comprised of one or moreline segments, and a two-dimensional polyline is a polyline comprised ofone or more line segments that lie within the same plane. Thus, it willbe appreciated that while the polylines are referred to astwo-dimensional polylines, such polylines may still be one-dimensionalentities in some instances, e.g., where such polylines include only oneline segment or where the segments of such polylines extend along thesame axis. It will also be appreciated that in some embodiments, theline segments of a polyline need not lie in the same plane.

Next, in block 404, the combined areas of the geometric primitiveswithin at least a subset of the cells of the 3D model are determined bysumming together the areas of individual geometric primitives withineach of the cells. Then, in block 406, a fracture abundance parameter isgenerated for the fracture network. For example, in some embodiments,the fracture abundance parameter may include a fracture density such asa P₃₂ value for one or more cells in the 3D model. In other embodiments,other values indicative of fracture abundance may be generated from thedetermined combined areas.

The fracture abundance parameter may then be used for various purposesin various embodiments of the invention. For example, as illustrated inblock 408, the fracture abundance parameter may be used in fluid flowsimulation using the same or a different 3D model of the subsurfaceformation. Further, as illustrated in block 410, the results of thefluid flow simulation may be used to perform various oilfieldoperations, e.g., drilling a production and/or injection well,developing a well plan, determining a well trajectory, managingproduction, mine planning, civil engineering (e.g.: slope stability,tunneling), geotechnical ground control applications, etc. In addition,a directly-calculated fracture abundance parameter such as thedirectly-calculated P₃₂ value described herein may be used in someembodiments to better constrain and validate a fracture network and/ordefine correction factors to correct a relative P₃₂ value inferred fromborehole data and interpolated in a 3D grid.

It will also be appreciated that the information generated during thevarious operations described above may also be visualized, e.g., withina graphical tool provided in an E&P platform, including bothvisualization of a generated fracture network as well as visualizationof fracture abundance parameters calculated therefor. Further, it willbe appreciated that the various operations may be performed by differenttools, and that the operations need not be performed by or within asingle tool.

Now turning to FIG. 6, as noted above a fracture network may be definedin block 402 of FIG. 5 in various manners in different embodiments. FIG.6, for example, illustrates a sequence of operations that “grows” orexpands three-dimensional fractures from two-dimensional polylines andrepresents those three-dimensional fractures using one or more geometricprimitives. In particular, in block 420 fractures are input as a set oftwo-dimensional polylines, i.e., lines defined by two distinct pointsand thus having a length along an axis extending between those points.The polylines may be generated, for example, from seismic data, fromoutcropping data, from borehole images, and, as discussed in greaterdetail below, from geomechanical data, among other sources. In someembodiments, for example, the 2D polylines may be defined within acommon plane such as a two-dimensional map representing a planar slicetaken through the subsurface formation, although the invention is not solimited.

Next, in block 422, each 2D polyline is grown or expanded in apredetermined direction and with a predetermined shape and aspect ratio,i.e., a ratio that controls the amount of growth in the predetermineddirection relative to the length of a polyline. The predetermined shapemay be selected from different potential shapes capable of representinga fracture. In the illustrated embodiment, for example, the shape may berectangular or elliptical, although the invention is not so constrained.Rectangular shapes may be favored for performance reasons, whileelliptical shapes may be favored for accuracy as many fractures have aprofile more closely matching that of an ellipse.

It will be appreciated that in some embodiments, expanding or growing apolyline along a predetermined direction may be considered to includeexpanding or growing the polyline in two opposite directions, e.g.,equidistant from the polyline, or in some instances, different distancesfrom the polyline. Further, expanding or growing a polyline along apredetermined direction generally results in the polyline being expandedwithin a plane that contains the polyline, referred to herein as acontaining plane for the polyline.

In different embodiments, a single direction, shape and aspect ratio maybe used to grow all polylines, while in other embodiments the direction,shape and/or aspect ratio may be varied for different polylines.Furthermore, the direction, shape and/or aspect ratio may be manuallyinput by a user in some embodiments, while in other embodiments, one ormore of these inputs may be determined programmatically. In someembodiments, for example, an optimizer may apply different inputs togenerate different three-dimensional fracture networks that may each beused to determine different fracture abundance parameters, and thesedifferent parameters may be used in fluid flow simulations and matchedagainst collected data to determine the combination of inputs that bestmatches observed data. In addition, it may even be desirable to utilizea randomized approach to generate directions, shapes and/or aspectratios for different polylines. As such, it will also be appreciatedthat the respective containing planes of different polylines may in someembodiments extend in a same direction or different directions relativeto a common plane within which the polylines are disposed, and further,in some embodiments, the respective containing planes may besubstantially orthogonal to such a common plane, e.g., beingsubstantially vertical relative to a substantially horizontal commonplane.

Next, in block 424, each grown 2D polyline may be transformed into aplurality of geometric primitives, e.g., triangles, to represent thegrown shape. Then in block 426, the geometric primitives may optionallybe output for visualization or other purposes. For example, in oneembodiment, the geometric primitives may be output in a TSURF fileformat for import and display in the PETREL E&P platform.

With further reference to FIGS. 7A-7D further illustrate thetransformation of 2D polylines into 3D sets of geometric primitives, andin the case where the 2D polylines are provided in the form of ahorizontal digitized fracture map such as may be generated from seismicor outcrop data, and grown in a vertical direction. FIG. 7A, inparticular, illustrates a fracture map 430 including a pair ofintersecting 2D polylines 432. FIGS. 7B, 7C and 7D respectivelyillustrate the transformation of polylines 432 into rectangular,elliptical and circular shapes, respectively.

As illustrated in FIG. 7B, for example, polylines 432 may be grown intorectangular shapes 440, each formed from four points or nodes 442 andtwo triangles 444. Likewise, as illustrated in FIG. 7C, polylines 432may alternately be grown into elliptical shapes 450, each formed from 13points or nodes 452 and 12 triangles 454. FIG. 7D also illustratescircular shapes 460, which are a special case of elliptical shapes wherethe radius An (semi-axis longest of an ellipse) and Bn (semi-axisshortest of an ellipse) are equal. However, fracture growth is notlimited to a certain number of nodes and triangles although highernumbers of nodes and triangles may lead to greater computationalresource requirements and/or computation times.

As noted above, the amount of growth may be constrained by an aspectratio, and as such, The starting and ending points of a 2D polyline andthe segment length may be used to expand a fracture according to anaspect ratio (Asp) as follows:

bn=an×Asp

where an is the fracture length divided per two and Asp is the inputaspect ratio.

Now returning briefly to blocks 404-406 of FIG. 5, once a fracturenetwork is defined, a fracture abundance parameter may be calculated fora fracture network in a number of different manners consistent with theinvention. Further, in some embodiments, a 3D observation grid may begenerated after defining a fracture network based upon the minimum andmaximum longitude/latitude and depth of the fracture network, and usinga selected unit cell size to provide the desired resolution for fractureabundance parameter calculations.

FIG. 8 next illustrates an example sequence of operations 480 suitablefor implementing blocks 404 and 406. In these examples, it assumed thatthe fracture network is derived from 2D polylines in a horizontalfracture map and grown in a vertical direction, and that the fractureabundance parameter calculated is a P₃₂ fracture density value for eachcell within an observation grid.

The calculation of P₃₂ in the 3D grid may in some embodiments beperformed by column along the vertical Z-axis, and in some embodiments,may organize or store geometric primitives from the fracture network inan octree or other spatially-organized data structure to optimizecalculations. Sequence of operations 480 begins in block 482 by creatinga new 3D grid property for a P₃₂ value. For each cell i,j,k (block 484),an Area_Sum variable is initialized to zero (block 486). Next, for eachfracture in the fracture network (block 488) and for each geometricprimitive in the fracture (block 490), the sequence may call isClipInsideCell function (block 492) to create a clipped primitiveincluding only that portion of the primitive that is inside the currentcell. Block 494 then calls an AreaFromProjections function (discussed ingreater detail below) on the clipped primitive to calculate the area ofthe primitive, and the result of this function is added to the Area_Sumvariable (block 496). This process is then repeated for every primitivein every fracture, resulting in Area_Sum storing the combined areas ofthe fractures within the cell. As such, block 498 divides Area_Sum bythe Unit Volume of the cell, resulting in the determination of the P₃₂value for that cell. Each cell in the grid is thereafter processed in asimilar manner, and the result is returned in block 499 as a 3D matrixof P₃₂ values.

In addition, as noted above, a generated fracture abundance parametermay be used for visualization, among other purposes. FIG. 9, forexample, illustrates two visualizations 550, 552 of a 3D volume or gridused to calculate a P₃₂ fracture density value for the 2D polylines 432illustrated in FIG. 7A and grown into rectangular shapes as illustratedin FIG. 7B. In visualization 550, the distribution of the P₃₂ fracturedensity parameter throughout the full grid is illustrated, while invisualization 552, the distribution is limited to a horizontal layerthrough the grid. Shadings or colors (mapped in legend 554) denote thevarying values of the P₃₂ parameter.

Now turning to FIGS. 10-12, in some embodiments of the invention,geometric primitive projection may be used to reduce the computationalresources and/or the latency associated with fracture abundanceparameter determinations, e.g., to implement the AreaFromProjectionsfunction discussed above. As noted above, fracture abundance parameterdeterminations may be based in part on determining a combined sum of theareas of geometric primitives such as triangular elements within eachcell or volume of a three-dimensional observation grid. Consequently, inmany embodiments, a fundamental operation that generally consumes asignificant portion of the employed computational resources isevaluating the area of a triangle in a cell, with the understanding thatthe triangle can cut the cell and thus project at least partiallyoutside of the cell. Conventional approaches to area determinations mayuse simplified fracture geometries, e.g., usually vertical and with arectangular shape, in order to reduce computational resources for theentire grid (which in some instances may contain millions of cells). Assuch, the accuracy that may otherwise be achieved using more complex andmore realistic shapes to model fractures (e.g., elliptical shapes and/orshapes that project in non-vertical directions) may need to besacrificed in order to achieve practical runtimes on moderately powerfulcomputer systems.

Some embodiments consistent with the invention, on the other hand, mayincorporate primitive projection to accelerate the determination of thearea of a geometric primitive such as a triangular element inside acell, such that the evaluation of fracture abundance may include atleast the operations of defining a fracture network within a pluralityof cells of a three-dimensional model of a subsurface formation using aplurality of geometric primitives, determining an area of the pluralityof geometric primitives within at least a subset of the plurality ofcells by summing areas of individual geometric primitives within each ofthe subset of cells, including determining an area of a first geometricprimitive among the plurality of geometric primitives within a firstcell in the subset of cells by projecting the first geometric primitiveonto each of first, second and third orthogonal planes respectivelyaligned with faces of the first cell to define respective first, secondand third projections and calculating areas of each of the first, secondand third projections, and determining a fracture abundance parameterfor the fracture network from the determined area of the plurality ofgeometric primitives. In addition to reducing computation time and/orcomputational resources, the herein-described technique may also in someembodiments shift the barrier to evaluate any triangular element of anyorientation in a 3D Cartesian space, such that rapid calculations may bemade of planar triangular elements of any orientation, and generallywithout involving classical heavy trigonometric algorithms to calculatethe area. Further, in some embodiments the area of any subsurfacestructure capable of being represented by triangular elements, e.g.,faults, fractures, horizons, etc., may be determined in a fast andefficient manner using the herein-described techniques, so theherein-described techniques may also be used for evaluating a subsurfaceformation by in part defining a subsurface structure within a pluralityof cells in a three-dimensional model of the subsurface formation usinga plurality of geometric primitives, determining an area of theplurality of geometric primitives using projection in the mannerdescribed herein, and determining a subsurface structure parameter forthe subsurface structure (e.g., a fracture abundance parameter for afracture network, or another parameter suitable for the particularsubsurface structure being modeled) from the determined area of theplurality of geometric primitives.

Primitive projection, in this regard may be considered to refer to anoperation that projects a shape of any arbitrary orientation within athree-dimensional cell onto a plane that is aligned with a face of aregular cubic cell. It will be appreciated that a face of a regularcubic cell is generally parallel to a plane formed by two of the threeaxes of a three-dimensional Cartesian coordinate system, e.g., wherepoints or nodes are identified by (x, y, z) values onmutually-orthogonal X, Y and Z axes, each cell will generally have twofaces parallel with each of XY, YZ and ZX planes defined by the X, Y andZ axes. Projection onto a plane aligned with a face of a regular cubiccell may therefore include projection onto a plane that is eithercoextensive with or parallel to a face of a cell, and thus coextensivewith or parallel to the XY, YZ or ZX planes defined for a grid ofregular cubic cells.

Projection may be further explained within the context of FIGS. 10-11.FIG. 10, in particular illustrates the determination of the length L ofan arbitrarily oriented one-dimensional line within a two-dimensionalplane through projection of the line onto the two orthogonal axes X andY. The nodes or endpoints of the line have coordinates (x₁, y₁) and (x₂,y₂), and it may be seen that projecting the line onto the X and Y axesgenerates two projections having lengths of L_(x)=(x₂−x₁) andL_(y)=(y₂−y₁). Through the application of the Pythagorean theorem thelength L of the line is related to the lengths of the projections by therelationship L²=L_(x) ²+L_(y) ², so the length L may be determined bytaking the square root of the sum of the lengths of the projections.

FIG. 11 illustrates an extension of this principle into athree-dimensional space, where the area A of an arbitrarily orientedtwo-dimensional planar shape 560 within a three-dimensional volume maybe determined through projection of the shape onto the three orthogonalplanes XY, ZX and YZ planes to form three projections 562, 564 and 566having areas A_(xy), A_(zx) and A_(yz) respectively. The area A of shape560, in particular, is related to the areas of projections 562, 564 and566 based upon the relationship A²=A_(xy) ²+A_(zx) ²+A_(yz) ², so thearea A may be determined by taking the square root of the sum of theareas of the projections.

A net effect of projecting a shape onto a plane aligned with a face of aregular cubic cell is that all points or nodes of the projection is thereduction of the 3D problem into a simple 2D problem, thus simplifyingthe determination of the area of a projection into a lesscomputationally-expensive operation. The location of each point or nodeof a projection of a shape thus may be represented by the other twocoordinates. Consequently, assuming that shape 560 is defined by threepoints (x₁, y₁,, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃), the projectionsonto the three planes XY, ZX and YZ may be considered to be defined bypoints:

XY projection: (x₁, y₁), (x₂, y₂) and (x₃, y₃)

ZX projection: (z₁, x₁), (z₂, x₂) and (z₃, x₃)

YZ projection: (y₁, z₁), (y₂, z₂) and (y₃, z₃)

Consequently, instead of performing complex computations to determinethe area of a triangle inside a three-dimensional cell, the area may bedetermined by projecting the triangle onto the three principal planesand sum the squares of the resulting projected areas.

It should also be appreciated, however, that clipping may also beperformed in connection with projection in order to determine the areaof a primitive within a cell, generally prior to projecting theprimitive. FIG. 11, for example, illustrates the clipped portions ofboth the primitive 560 and each projection 562-566 using darker shadingthan the portions that fall outside of the cell. Consequently, thecoordinates of each point of the primitives may be compared with thecoordinates of the boundary of the cell to replace any point disposedoutside of the boundary of the cell with one or more points along theboundary of the cell. For example, as illustrated by the XY projection562, assuming that the projection without clipping would have threepoints P₁, P₂and P₃ and with point P₃ lying outside of the cell, thispoint may be replaced by points P₄ and P₅ to create a projected shapedefined by points P₁, P₂, P₄ and P₅. In addition, while various areacalculations may be used to determine the areas of clipped projections,in one embodiment the areas of clipped projections may be determined bysplitting a clipped projection into a plurality of triangles and summingthe areas of the triangles forming the clipped projection.

Now turning to FIG. 12, this figure illustrates an example sequence ofoperations 570 for performing projection-based fracture abundanceparameter calculations in the manner discussed above, and in particularto determine a P₃₂ fracture density value for each cell in anobservation grid. Sequence 570, in the illustrated embodiment, utilizesan octree or other data structure to spatially organize geometricprimitives, here triangles, of a defined fracture network, and therebyfacilitate lookup of the triangles that are within each cell. Varioustypes of data structures and/or lookup algorithms, including algorithmsbased on other types of binary and/or spatially-partitioned trees, maybe used in other embodiments.

Block 572 initially builds an octree of the fractures in the fracturenetwork. Then, for each cell C of the grid (block 574), the octree isaccessed to generate a set F of all fractures that at least partiallyintersect the cell C (block 576). A combined area variable A_(c) is thenreset (block 578), and each fracture fin set F (block 580), and eachtriangle t defining fracture f (block 582) is processed by projectingthe area of the triangle t onto planes XY, ZX and YZ (block 584, 586 and588), with the areas of the projections stored in A_(xy), A_(zx) andA_(yz) respectively. The areas are then summed and a square root istaken of the sum, with the result added to the combined area variableA_(c) (block 590). Then, for each cell C, the combined area variable Acis divided by the unit volume of the cell V_(C) to generate the P₃₂fracture density value for the cell (block 592). As a result of sequence570, therefore, a P₃₂ fracture density value is generated for each cellof the grid.

Now turning to FIG. 13, in some embodiments fracture abundanceevaluation may be based at least in part on geomechanical simulationbased on mechanical properties of a subsurface formation. For example,using an engine such as the FAULT MODELER engine available fromSchlumberger Ltd. and its affiliates, fracture density and/or fractureheight may be estimated from geomechanical simulation using mechanicalproperties of a subsurface formation, e.g., as collected from welllogging. For example, a balance energy operation may be used to estimatea P₁₀ fracture density and fracture height from well log data in someembodiments.

FIG. 13, in particular, illustrates an example sequence of operations600 for evaluating fracture abundance based on geomechanical simulationbased on mechanical properties. First, in block 602, a P₁₀ fracturedensity and fracture height for a subsurface formation may be determinedfrom mechanical properties derived from well log data, e.g., one or moreof Young's modulus, Poisson's ratio, friction coefficient, cohesion,fault dip, effective vertical stress, fluid pressure, and crack surfaceenergy, among others. Such calculations may be based on a balance energyapproach, and may be performed, for example, using geomechanicalsimulation functionality available in the PETREL, TECHLOG or FAULTMODELER software available from Schlumberger and its affiliates,although it will be appreciated that the invention is not limited to usewith such software.

Based upon the results of block 602, an input file may be createdincluding 2D polyline representations of fractures associated withfracture height, and taken along a vertical trace corresponding to thewell from which the geomechanical properties were obtained that extendsalong the well (block 604), and then each 2D polyline may be grown in asimilar manner to that described above in connection with FIG. 6, butwith the direction of growth being horizontal for a vertical well (block606). An aspect ratio may also be used to control the growth, andvarious shapes, including rectangular or elliptical shapes. Againsimilar to FIG. 6, the grown shapes may be transformed into geometricprimitives (block 608), and then similar to FIG. 5, a fracture abundanceparameter for the fracture network, e.g., a P₃₂ fracture density valuefor each cell, may be determined (block 610). Fluid flow simulation(block 612) and/or an oilfield operation (block 614) may then beperformed, again similar to FIG. 5.

In addition, visualization may be also be performed after variousoperations from FIG. 13. For example, FIG. 14 illustrates avisualization 620 of fracture growth around an example well based upongeomechanical properties, while visualization 622 illustrates a verticalsection of an observation grid containing the directly-calculated “true”P₃₂ value, with legend 624 mapping the shading to different ranges ofP₃₂ values.

Therefore, some embodiments of the invention support the evaluation oftrue P₃₂ fracture density based on a 1D geomechanical method. Byestimating the true P₃₂, reservoir simulations in some embodiments maybe better constrained, particularly for vertical wells that may runparallel to the fracture network, and may not detect fracture at in somecircumstances leading to an optimized production of the reservoirthrough flow simulation. In addition, in some embodiments, the resultsof the aforementioned evaluation may be used for other purposes, e.g.,for derisking, drilling and fracture connectivity. This is particularlytrue in certain situations. For example, as illustrated in FIG. 15, welllog data from a vertical well A may detect one fracture along layer 2while nothing is observed in layers 3, 4 and 5. Well B may detect afracture on layer 4, with nothing observed in the other layers. Further,well C may not detect a fracture at all. The herein-described techniquesmay therefore address these situations and estimate 3D fractureabundance with better prediction along wells, which may be used topopulate a 3D grid for fracture network generation instead of a directconventional measure of fracture abundance such as a P_(10c) value.

Various modifications may be made in other embodiments. For example, itwill be appreciated that three-dimensional fracture abundance evaluationin some embodiments may use area determination operations other than theherein-described projection-based area determinations, as well as thatprojection-based area determinations may have other applications beyondthat of fracture abundance evaluation. Further, as noted above, variousoperations may be used to generate or define a fracture network, so theinvention is not limited to the particular geomechanicalsimulation-based approach disclosed herein, and further, otherthree-dimensional fracture abundance evaluation approaches beyond thosedescribed herein may be used to evaluate fracture abundance usingmechanical properties.

Although the preceding description has been described herein withreference to particular means, materials, and embodiments, it is notintended to be limited to the particular disclosed herein. By way offurther example, embodiments may be utilized in conjunction with ahandheld system (i.e., a phone, wrist or forearm mounted computer,tablet, or other handheld device), portable system (i.e., a laptop orportable computing system), a fixed computing system (i.e., a desktop,server, cluster, or high performance computing system), or across anetwork (i.e., a cloud-based system). As such, embodiments extend to allfunctionally equivalent structures, methods, uses, program products, andcompositions as are within the scope of the appended claims. Inaddition, while particular embodiments have been described, it is notintended that the invention be limited thereto, as it is intended thatthe invention be as broad in scope as the art will allow and that thespecification be read likewise. It will therefore be appreciated bythose skilled in the art that yet other modifications could be madewithout deviating from its spirit and scope as claimed.

What is claimed is:
 1. A method of evaluating fracture abundance in asubsurface formation, the method comprising: defining a fracture networkwithin a plurality of cells of a three-dimensional model of thesubsurface formation using a plurality of geometric primitives;determining an area of the plurality of geometric primitives within atleast a subset of the plurality of cells by summing areas of individualgeometric primitives within each of the subset of cells; and determininga fracture abundance parameter for the fracture network from thedetermined area of the plurality of geometric primitives.
 2. The methodof claim 1, wherein defining the fracture network includes expandingeach of a plurality of two-dimensional polylines representing fracturesin the subsurface formation within a respective containing plane.
 3. Themethod of claim 2, wherein defining the fracture network furtherincludes representing each two-dimensional polyline by multiplegeometric primitives disposed in the respective containing plane.
 4. Themethod of claim 2, wherein the plurality of two-dimensional polylinesare disposed in a common plane, and wherein the respective containingplanes extend in a same direction relative to the common plane.
 5. Themethod of claim 4, wherein the respective containing planes aresubstantially orthogonal to the common plane.
 6. The method of claim 5,wherein the respective containing planes are substantially vertical andthe common plane is substantially horizontal.
 7. The method of claim 4,wherein the respective containing planes extend in different directionsrelative to the common plane.
 8. The method of claim 2, whereinexpanding each of the plurality of two-dimensional polylines includesusing an aspect ratio to constrain expansion of each of the plurality oftwo-dimensional polylines within the respective containing planesrelative to fracture length.
 9. The method of claim 2, wherein each ofthe plurality of geometric primitives is a triangular element.
 10. Themethod of claim 9, wherein expanding each of the plurality oftwo-dimensional polylines includes expanding a first two-dimensionalpolyline among the plurality of two-dimensional polylines into asubstantially rectangular shape represented by first and secondtriangular elements defined by four nodes.
 11. The method of claim 9,wherein expanding each of the plurality of two-dimensional polylinesincludes expanding a first two-dimensional polyline among the pluralityof two-dimensional polylines into a substantially elliptical shaperepresented by twelve triangular elements defined by thirteen nodes. 12.The method of claim 11, wherein the substantially elliptical shape is asubstantially circular shape.
 13. The method of claim 1, whereindetermining the area of the plurality of geometric primitives within thesubset of the plurality of cells includes clipping individual geometricprimitives that are partially within each of the subset of cells. 14.The method of claim 13, wherein determining the area of the plurality ofgeometric primitives within the subset of the plurality of cells furtherincludes: organizing the plurality of geometric primitives within aspatially-organized data structure; and accessing thespatially-organized data structure when summing areas of individualgeometric primitives within each of the subset of cells to determinewhich of the plurality of geometric primitives are at least partiallywithin each of the subset of cells.
 15. The method of claim 1, whereindetermining the fracture abundance parameter includes determining afracture density within each of the subset of cells by dividing thesummed areas of individual geometric primitives therein by a volumethereof.
 16. The method of claim 1, wherein determining the fractureabundance parameter includes determining a directly-calculated P₃₂fracture density within each of the subset of cells by dividing thesummed areas of individual geometric primitives therein by a volumethereof.
 17. The method of claim 1, further comprising running a fluidflow simulation using the determined fracture abundance parameter toestimate fluid flow through the fracture network.
 18. The method ofclaim 17, further comprising performing an oilfield operation based upona result of the fluid flow simulation.
 19. An apparatus, comprising: atleast one processing unit; and program code configured upon execution bythe at least one processing unit to evaluate fracture abundance in asubsurface formation by: defining a fracture network within a pluralityof cells of a three-dimensional model of the subsurface formation usinga plurality of geometric primitives; determining an area of theplurality of geometric primitives within at least a subset of theplurality of cells by summing areas of individual geometric primitiveswithin each of the subset of cells; and determining a fracture abundanceparameter for the fracture network from the determined area of theplurality of geometric primitives.
 20. A program product, comprising: acomputer readable medium; and program code stored on the computerreadable medium and configured upon execution by at least one processingunit to evaluate fracture abundance in a subsurface formation by:defining a fracture network within a plurality of cells of athree-dimensional model of the subsurface formation using a plurality ofgeometric primitives; determining an area of the plurality of geometricprimitives within at least a subset of the plurality of cells by summingareas of individual geometric primitives within each of the subset ofcells; and determining a fracture abundance parameter for the fracturenetwork from the determined area of the plurality of geometricprimitives.